You can also use the term "speedrun" more generally, for any recording where you are trying to achieve a particular goal in the quickest possible time.

This goal can take many forms; e.g.:
* reaching the exit on skill 1 (ITYTD Speed);
* reaching the exit on skill 3 without killing any monsters (HMP Lemmings);
* reaching the exit on skill 4 with fast monsters, leaving no monsters alive (not counting lost souls) and using only weapons 1 and 2 (UV Fast Tyson);
etc., etc.

This definition is the one implied by such site names as "Tool-Assisted Speedruns" and "Doomed Speed Demos Archive" - these sites do not of course exclude Max, NM100S, etc.